LESSONS IN ASTRONOMY. 



159 



Jfow whi'ii any planet is in that part of its orbit which in 

 i 1 is said to bo in . 



o Greek words signifying "near tho BUD;" and when iit the 

 it ia said to be in aplulion, or away 



au. 



a o A, or half the major aria, ia called the mean 

 :ui J thin it in which is given in all tables of the solar 



ho distance of tho planeta. 



; . had long been noticed that the apparent daily motion 

 . :L was greater at aomo times than at others; and the 

 too, weru found not to move exactly at a uniform rato, 

 ing more rapid when in perihelion than when in 

 er parts of thoir orbits. Kopler accordingly determined to 

 uiul discover the law which established the relation between 

 distances and their speeds. This link was manifestly 

 ting to enable him to foretell the exact place the sun or a 



mid occupy at any given moment, for though he had 

 out their paths, yet, as their speeds varied, he could not 



in what part of those paths they would bo unless he knew 

 amount of this variation. 

 This work he accomplished with far less difficulty than he had 

 rienced in the discovery of his first groat law, and he soon 

 luuccd his second law, which teaches that 



velocity of any planet at every point of its orbit is such that 



.<-<iwn from it to the sun always describes equal spaces in 

 I times. This imaginary line, joining the centres of the sun 

 planet, is called the radius vector. 



This law may bo easily understood by reference to Fig. 2, 

 s-may be taken to represent the position of the sun, and 

 c D E F G the successive positions occupied by the planet 

 equal intervals, so that it passes from A to B in the same 

 period as from B to c or from c to D. 



Now join these points with s, and wo shall find that tho space 

 A s B passed over by the radius vector in one period is exactly 

 equal to tho space B 8 c passed over in the next, and to each 

 of the other spaces c s D, D s E, etc. We see thus that the 

 rate of the planet's motion when near c is greater than as it 

 approaches A. The same would be found to hold good if we 

 had divided the orbit into spaces passed over in one day, or in 

 any other peripd. This law, then, together with the former 

 one, enables us exactly to calculate the place of any planet at 

 any time. Kepler, however, was not content with this : as he 

 gazed on tho different members of our system, he found so many 

 points of resemblance in their movements that he conceived 

 there must be some general law connecting the whole into one 

 grand unity. They all had the sun as one focus of their orbits, 

 they all moved in elliptical orbits around that body and in the 

 same direction, and all obeyed the same law as to rate of 

 motion ; he fancied, therefore, that some intimate bond of union 

 it exist between them, and set himself to discover it. 



This was a more difficult task than either of the former had 

 ID, for there he had certain facts given, and had merely to 

 form a theory that would explain them all ; now he had to grope 

 about for some law the very existence of which he only sus- 

 pected, nor could he tell whether it connected their distances, 

 their sizes, their periods, or their densities. He conjectured, 

 however, that if there was any such relationship, it would pro- 

 bably bo between their distances and their periods of revolution, 

 more especially as his second law showed that in the case of each 

 individual planet these quantities varied in a definite proportion. 

 Accordingly, he commenced to compare their distances with their 

 periods, but not the faintest clue could ho find in this way to 

 guide him ; ho then tried various multiples of these quantities, 

 but with no better success. So firmly, however, was ho con- 

 vinced that some such law did exist, that ho tried fresh com- 

 binations and multiples ; yet could find no relation whatever. 

 He then compared the squares and tho cubes, but, though 

 trifling approximations were at times found, they were far from 

 somplete, and ho had still to try again. It now occurred to him 

 to compare the squares of the periods with the cubes of the 

 distances, and these calculations he accordingly worked out, 

 but failed to detect any resemblance, owing, as afterwards ap- 

 peared, to an error in some of his figures. The question now 

 began to appear hopeless, and was for a time laid aside, many 

 anxious years having been spent in vain attempts to solve it ; 

 but still at times Kepler would almost instinctively look back 

 "'"r his old calculations, and in doing so one day he detected 

 error above referred to. He accordingly went again over tho 



whole work, and with intense joy found the reault agree in the 

 most marked way. Tho name oalonlations were then made for 

 the other planeta, and atill found to hold good, and thus the 

 remaining law which govern* oar universe was at hutt din- 

 covered. Only thoae who have themselves toiled on year after 

 year in a aearoh which often appeared hopeless, can realise 

 the triumph of the philosopher a* he than discovered the laws 

 of the heavena, and reduced all the apparently irregular motion* 

 of the heavenly orbs to three great but simple lawn. 



The third law may be stated thus: The squares of the 

 periodic times of any two planet* bear the tame proportion to 

 each other at the cubes of their mean distances. 



Thus, if we know the distance of a planet, we can calculate 

 approximately ita time of revolution round the sun ; and, on 

 the other hand, if we know its time we can ascertain its dis- 

 tance. When the distances and periods of tho different 

 members of our system have been given, the student will be 

 able to check this rule for himself, and will find that the propor- 

 tion holds true to within a comparatively small amount. As an 

 illustration, however, he may take the distances and periods of 

 Venus and the Earth, which may be set down in round numbers 

 as follows : 



Venus 



Earth 



Period. 

 224 days 

 365 



Dittance. 

 68,000,000 miles. 

 95,000,000 



The proportion between the periods here ia j$, and that be- 

 tween the distances gjj. If now we take the square of the 

 former quantity, we shall find that it ia nearly equal to the cube 

 of the latter. It must, however, be remembered that the 

 numbers above given are mere approximations ; the exact figures 

 will be given in a subsequent lesson. 



Almost contemporary with Kepler there lived another great 

 philosopher and astronomer, Galileo by name, chiefly memorable 

 now as having been the first to construct the astronomical 

 telescope, though his powers were such as would have ensured 

 his renown, even had this great discovery not been made by 

 him. He was born in 1564, and became a philosophical teacher 

 at Pisa. Here he soon rendered himself remarkable by hia 

 violent opposition to some of the teachings of Aristotle, which he 

 proved by experiment to be incorrect. This brought upon him 

 much odium, and even persecution ; but though he thus op- 

 posed the received views on mechanical subjects, he continued 

 for some time a firm believer in the Ptolemaic system, and 

 even refused to hear any explanation of the viewa and theories 

 of Copernicus. After a time, however, he aaw the folly of this, 

 and commenced a careful inquiry, the result of which was that 

 he became an ardent upholder of the new system. 



In the early part of the seventeenth century, Galileo heard 

 of a discovery which had been made by an instrument-maker 

 in Holland, by which distant objects could be made distinctly 

 visible. He therefore made every inquiry, and, after several 

 trials, at last succeeded in manufacturing a telescope which 

 possessed a magnifying power of 30. 



This he first directed towards the moon, and here he at once 

 detected many points of resemblance to the earth : there were 

 rugged mountainous parts and lofty elevations ; level plains 

 likewise, which were at first called seas, were observed. A 

 greater discovery was, however, made when on the 7th of January, 

 1610, he directed his magic tube towards the planet Jupiter. 

 Not only did it present to him a brilliant disc streaked across 

 with dark bands, but close to it were three small stars almost 

 in a straight line. These wore at first supposed to be merely 

 fixed stars ; on the following evening, however, when the tele- 

 scope was again directed to the planet, it was observed that 

 they had moved along with it, and had also changed their 

 positions with respect to each other. Here, then, was evidently 

 some new discovery, and most anxiously did Galileo await the 

 recurrence of a clear evening to enable him to decide the 

 matter. The next view satisfied him that they were in reality 

 moons accompanying the planet, and further, he found that 

 there were four of them. 



Intense excitement was created among astronomers by this 

 discovery, some urging the absurdity of increasing the number 

 of the heavenly bodies beyond the sacred number seven, and 

 others angry at the man who attempted to depose the earth 

 from its position of dignity, by asserting that Jupiter had 

 four satellites while the earth had only one. Somo even ro- 



